To store cooked turkey for leftovers, divide into smaller portions and refrigerate or freeze in shallow, covered containers. This allows the meat to cool quickly, says Kathy Bernard, acting manager of the USDA's Meat and Poultry Hotline. Store cooked turkey in the refrigerator for three to four days, or the freezer for up to six months for best quality. For slices of cooked ham, three to five days in the refrigerator is acceptable, or wrap well and keep in the freezer for one to two months.